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Characterizations of intrinsic volumes on convex bodies and convex functions
[SNAP-2022-011-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2022-12-08)
If we want to express the size of a two-dimensional shape with a number, then we usually think about its area or circumference. But what makes these quantities so special? We give an answer to this question in terms of ...
Waves and Incidences
[SNAP-2024-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2024-04-09)
The wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each ...
Randomness is Natural - an Introduction to Regularisation by Noise
[SNAP-2024-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2024-05-22)
Differential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic ...
Cutoff Phenomenon: Surprising Behaviour in Card Shuffling and other Markov Chains
[SNAP-2023-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2023-12-21)
This snapshot compares two techniques of shuffling a deck of cards, asking how long it will take to shuffle the cards until a “well-mixed deck” is obtained. Surprisingly, the number of shuffles can be very different for ...
Cutoff-Phänomen: überraschendes Verhalten beim Kartenmischen und bei weiteren Markovketten
[SNAP-2023-005-DE] (Mathematisches Forschungsinstitut Oberwolfach, 2024-10-22)
Dieser Schnappschuss vergleicht zwei Arten des Kartenmischens und untersucht, wie lange es dauert einen "gut gemischten" Kartenstapel zu erhalten. Überraschenderweise kann das Mischverhalten auch für sehr ähnlich ausschauende ...
Voronoi Cells: Or How to Find the Nearest Bakery
[SNAP-2024-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2024-09-05)
Deciding which mall, hospital or school is closest to us is a problem we face everyday. It even comes on holidays with us, when we optimize our plans to make sure that we have enough time to visit all the attractions we ...
Uncertainty as an Ingredient in Financial Modeling
[SNAP-2024-004-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2024-12-17)
Uncertainty - as opposed to risk - is used to describe events to which we are not able to assign a probability due to lack of information. Instead of assigning a probability to an uncertain event, we only assume that such ...
Truncated Fusion Rules for Supergroups
[SNAP-2025-001-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2025-02-03)
In the '70s, physicists introduced a new type of symmetry – supersymmetry – to address some unresolved issues in particle physics models. Its mathematical foundations involve the representation theory of the associated ...